This work describes the design and evaluation of a proposal to use Classroom Response Systems (CRS), intended to promote participative classes of Mathematics at University. The proposal is based on Problem Based Learnig (PBL) and uses Robert's six hypotheses for mathematical teaching-learning. The results show that PBL is a relevant strategy to…

Since the mid-20th century, the standard U.S. high school and college math curriculum has been based on two years of algebra and a year of geometry, preparing students to take classes in pre-calculus followed by calculus. Students' math pursuits have been differentiated primarily by how far or how rapidly they proceed along a clearly defined…

This article discusses the conditions under which all solutions to x[double prime] + q(t)b(x) = f(t) are bounded on [0, [infinite]]. These results are generalizations of the linear case. A short discussion of the properties of bounded oscillatory solutions for both the linear and nonlinear cases when f(t) = 0, xb(x) greater than 0 and b[prime](x)…

Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the "Magnus expansion" (also known as "exponential perturbation theory") provides such unitary approximate solutions. The purpose is to illustrate the importance and…

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for…

This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation…

The Common Core State Standards for Mathematics (CCSSM) are founded on a long history of mathematics education research emphasizing the importance of teaching mathematics for understanding. The CCSSM along with the National Council of Teachers of Mathematics (NCTM) recommend the use of technology in the teaching of mathematics. New mobile…

Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly…

The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

Over the past three decades, American high school students' course taking has rapidly intensified. Between 1982 and 2004, for example, the proportion of high school graduates who earned credit in precalculus or calculus more than tripled. In this article, the authors investigate the consequences of mathematics curricular intensification for social…

This paper uses a relatively large dataset of the stated academic major preferences of economics majors at a relatively large, not highly selective, public university in the USA to identify the "discouraged-business-majors" (DBMs). The DBM hypothesis addresses the phenomenon where students who are screened out of the business curriculum often…

The study compared the effect of two adaptations of a scientific article on students' comprehension and use of scientific inquiry skills. One adaptation preserved as much as possible the canonical form of the original article (APL, Adapted Primary Literature) and the other was written in a more narrative mode typical of secondary literature (SL).…

Institutions find success with Pearson Education's MyMathLab. The Department of Mathematical Sciences at the University of Memphis (UM) reported a narrowing of the achievement gap between Black and White students. According to the study conducted by UM professors and titled "The Effectiveness of Blended Instruction in Postsecondary General…

In this article an application of conformal mapping to aerofoil theory is studied from a geometric and calculus point of view. The problem is suitable for undergraduate teaching in terms of a project or extended piece of work, and brings together the concepts of geometric mapping, parametric equations, complex numbers and calculus. The Joukowski…